Monitoring activities using video data is an important surveillance problem. A special scenario is to learn the pattern of normal activities and detect abnormal events from a very low resolution video where the moving objects are small enough to be modeled as point objects in a 2D plane. Instead of tracking each point separately, we propose to model an activity by the polygonal 'shape' of the configuration of these point masses at any time t, and its deformation over time. We learn the mean shape and the dynamics of the shape change using hand-picked location data (no observation noise) and define an abnormality detection statistic for the simple case of a test sequence with negligible observation noise. For the more practical case where observation (point locations) noise is large and cannot be ignored, we use a particle filter to estimate the probability distribution of the shape given the noisy observations up to the current time. Abnormality detection in this case is formulated as a change detection problem. We propose a detection strategy that can detect both 'drastic' and 'slow' abnormalities. Our framework can be directly applied for object location data obtained using any type of sensors - visible, radar, infrared or acoustic.